In the US most physicians, surgeons and dentists are addressed as "doctor". Very few other professionals receive the same title. In the UK, however, surgeons and dentists seem to prefer to be referred to as Mr. If that is true, why? And who is addressed as Dr. in the UK? Those who hold doctoral degrees only?
My brother has a doctoral degree: it's a DM rather than MD, and he's called Doctor.
In fact, he was called Dr Leach when he gained his first BM degree and registered with the General Medical Council: that combination allowed him to practice and he gained the title "Doctor". Many medical doctors don't have a doctoral degree.
Surgeons have a similar process. They gain a first degree — perhaps a BM or probably BS or BDS — register to practise and gain the title "Mr" or "Mrs" (or "Miss": that's a choice women have in this case). They retain this surgeon's title even if they gain a doctoral degree.
This use of the title Mr or Mrs is not the same as the form of address "Mr/Mrs" that one might use of your next-door neighbour. It also only refers to surgeons. Physicians are always "Doctor" even without a doctoral degree.
An article in the British Medical Journal, reproduced in the US, explains the history and how Mr has evolved into the title for surgeons.